The Toffees fell behind on the stroke of half-time at Goodison Park when they were unable to properly clear a corner which ended when Craig Gardner dinked a ball into the area for Adam Johnson to come up with a superb half-volley from close range to knock the ball over an advancing Tim Howard for his first Mackem goal.
The scoreline remained at 1-0 until the 77th minute when Marouane Fellaini, fresh off a double against Fulham last week, received a pass from Leon Osman before turning and putting his effort through a crowd of players and across Simon Mignolet for the equaliser.
David Moyes' 400th match in charge of Everton then turned into a celebration when Osman and Fellaini again combined with the Belgian sending a backheel into the path of Nikica Jelavic to slot home from close range to sustain their 11-year unbeaten run against the Black Cats.
It was the Toffees' fifth win this campaign which allows them to go to 20 points from 11 outings as Martin O'Neill's Sunderland continue to hang perilously close to the drop zone with just nine points from 10 fixtures.
Goodison Park, Liverpool - 35,999